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The set S of square matrices of same order with respect to matrix addition is a
1. quasi group
2. semi group
3. group
4. abelian group?
1. quasi group
2. semi group
3. group
4. abelian group?
Most Upvoted Answer
The set S of square matrices of same order with respect to matrix addi...
Properties of the set S of square matrices:
- Quasi group:
A quasi group is a set with a binary operation that has unique solutions to both left and right division. In the set S of square matrices with matrix addition as the operation, it is not a quasi group because not all elements have unique left and right inverses.
- Semi group:
A semi group is a set with an associative binary operation. The set S of square matrices with matrix addition is closed under addition and satisfies the associative property. Therefore, it is a semi group.
- Group:
A group is a set with an associative binary operation, identity element, and inverses for each element. The set S of square matrices with matrix addition does not have inverses for each element, so it is not a group.
- Abelian group:
An abelian group is a group where the binary operation is commutative. The set S of square matrices with matrix addition is closed under addition and commutative, but lacks inverses for each element, so it is not an abelian group.
In conclusion, the set S of square matrices with respect to matrix addition is a semi group but not a group or an abelian group due to the absence of inverses for each element.
- Quasi group:
A quasi group is a set with a binary operation that has unique solutions to both left and right division. In the set S of square matrices with matrix addition as the operation, it is not a quasi group because not all elements have unique left and right inverses.
- Semi group:
A semi group is a set with an associative binary operation. The set S of square matrices with matrix addition is closed under addition and satisfies the associative property. Therefore, it is a semi group.
- Group:
A group is a set with an associative binary operation, identity element, and inverses for each element. The set S of square matrices with matrix addition does not have inverses for each element, so it is not a group.
- Abelian group:
An abelian group is a group where the binary operation is commutative. The set S of square matrices with matrix addition is closed under addition and commutative, but lacks inverses for each element, so it is not an abelian group.
In conclusion, the set S of square matrices with respect to matrix addition is a semi group but not a group or an abelian group due to the absence of inverses for each element.
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The set S of square matrices of same order with respect to matrix addition is a 1. quasi group 2. semi group 3. group 4. abelian group?
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The set S of square matrices of same order with respect to matrix addition is a 1. quasi group 2. semi group 3. group 4. abelian group? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about The set S of square matrices of same order with respect to matrix addition is a 1. quasi group 2. semi group 3. group 4. abelian group? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The set S of square matrices of same order with respect to matrix addition is a 1. quasi group 2. semi group 3. group 4. abelian group?.
The set S of square matrices of same order with respect to matrix addition is a 1. quasi group 2. semi group 3. group 4. abelian group? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about The set S of square matrices of same order with respect to matrix addition is a 1. quasi group 2. semi group 3. group 4. abelian group? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The set S of square matrices of same order with respect to matrix addition is a 1. quasi group 2. semi group 3. group 4. abelian group?.
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